This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hörmander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers.
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From the reviews of the second edition: "This is the second edition of Shubin’s already classical book. It provides a fairly short, highly readable nice introduction to microlocal analysis, with emphasis on its application to spectral theory … . For anybody who holds a first course in PDO and FIO we highly recommend … . The book is very well written, in simple and direct language. From the very basics at the beginning, the reader reaches a fairly advanced graduate level at the end." (Tibor Ódor, Acta Scientiarum Mathematicarum, Vol. 73, 2007)
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